Abstract
We consider the gauge invariance of the two-photon transition rate from the crystal ground state to exciton states in semiconductors in the framework of the Wannier model. We show that the non-locality correction in the velocity gauge is essential to preserve the gauge invariance. As a numerical example, we calculate in the length and in the velocity gauge the transition rates for the two-photon direct creation of 2 p excitons in a two-band semiconductor.
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